Calendar: 1875-1876 Page 581

GENERAL LITERATURE AND SCIENCE 577 VI -CufltB On the same base and on the same side of it there cannot be two triangles which have their sides which are terminated in one extremity of the base equal to one another and likewise those which are terminated in the other extremity If two triangles have two sides of the one equal to two sides of the other each to each and have also their bases equal the angle which is contained by the two sides of the one shall be equal to the angle which is contained by the two sides equal to them of the other To draw straight line at right angles to given straight line of unlimited length from given point without it Any two sides of triangle are together greater than tbe third side If straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same side of the line or makes the interior angles upon the same side together equal to two right angles the two straight lines shall be parallel to one another Parallelograms upon the same base and between the same parallels are equal to one another In any right-angled triangle the square which is described on the side subtending the right angle is equal to the squares described on the sides which contain the right angle If straight line be divided into any two parts the square of the whole line is equal to the squares of the two parts together with twice the rectangle contained by the parts In every triangle the square of the side subtending either of the acute angles is less than the squares of the sides contain- ing that angle by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular let fall upon it from the opposite angle and the acute angle 10 The angles in the same segment of circle are equal to one another 11 The opposite angles of any quadrilateral figure inscribed in circle are together equal to two right angles 12 If from any point without circle two straight lines be ο ο